c-----------------------------------------------------------------------
c\BeginDoc
c
c\Name: igraphdnconv
c
c\Description: 
c  Convergence testing for the nonsymmetric Arnoldi eigenvalue routine.
c
c\Usage:
c  call igraphdnconv
c     ( N, RITZR, RITZI, BOUNDS, TOL, NCONV )
c
c\Arguments
c  N       Integer.  (INPUT)
c          Number of Ritz values to check for convergence.
c
c  RITZR,  Double precision arrays of length N.  (INPUT)
c  RITZI   Real and imaginary parts of the Ritz values to be checked
c          for convergence.

c  BOUNDS  Double precision array of length N.  (INPUT)
c          Ritz estimates for the Ritz values in RITZR and RITZI.
c
c  TOL     Double precision scalar.  (INPUT)
c          Desired backward error for a Ritz value to be considered
c          "converged".
c
c  NCONV   Integer scalar.  (OUTPUT)
c          Number of "converged" Ritz values.
c
c\EndDoc
c
c-----------------------------------------------------------------------
c
c\BeginLib
c
c\Local variables:
c     xxxxxx  real
c
c\Routines called:
c     igraphsecond  ARPACK utility routine for timing.
c     dlamch  LAPACK routine that determines machine constants.
c     dlapy2  LAPACK routine to compute sqrt(x**2+y**2) carefully.
c
c\Author
c     Danny Sorensen               Phuong Vu
c     Richard Lehoucq              CRPC / Rice University 
c     Dept. of Computational &     Houston, Texas
c     Applied Mathematics 
c     Rice University           
c     Houston, Texas    
c
c\Revision history:
c     xx/xx/92: Version ' 2.1'
c
c\SCCS Information: @(#) 
c FILE: nconv.F   SID: 2.3   DATE OF SID: 4/20/96   RELEASE: 2
c
c\Remarks
c     1. xxxx
c
c\EndLib
c
c-----------------------------------------------------------------------
c
      subroutine igraphdnconv (n, ritzr, ritzi, bounds, tol, nconv)
c
c     %----------------------------------------------------%
c     | Include files for debugging and timing information |
c     %----------------------------------------------------%
c
      include   'debug.h'
      include   'stat.h'
c
c     %------------------%
c     | Scalar Arguments |
c     %------------------%
c
      integer    n, nconv
      Double precision
     &           tol
c
c     %-----------------%
c     | Array Arguments |
c     %-----------------%

      Double precision
     &           ritzr(n), ritzi(n), bounds(n)
c
c     %---------------%
c     | Local Scalars |
c     %---------------%
c
      integer    i
      Double precision
     &           temp, eps23
c
c     %--------------------%
c     | External Functions |
c     %--------------------%
c
      Double precision
     &           dlapy2, dlamch
      external   dlapy2, dlamch

c     %-----------------------%
c     | Executable Statements |
c     %-----------------------%
c 
c     %-------------------------------------------------------------%
c     | Convergence test: unlike in the symmetric code, I am not    |
c     | using things like refined error bounds and gap condition    |
c     | because I don't know the exact equivalent concept.          |
c     |                                                             |
c     | Instead the i-th Ritz value is considered "converged" when: |
c     |                                                             |
c     |     bounds(i) .le. ( TOL * | ritz | )                       |
c     |                                                             |
c     | for some appropriate choice of norm.                        |
c     %-------------------------------------------------------------%
c
      call igraphsecond (t0)
c
c     %---------------------------------%
c     | Get machine dependent constant. |
c     %---------------------------------%
c
      eps23 = dlamch('Epsilon-Machine')
      eps23 = eps23**(2.0D+0 / 3.0D+0)
c
      nconv  = 0
      do 20 i = 1, n
         temp = max( eps23, dlapy2( ritzr(i), ritzi(i) ) )
         if (bounds(i) .le. tol*temp)   nconv = nconv + 1
   20 continue
c 
      call igraphsecond (t1)
      tnconv = tnconv + (t1 - t0)
c 
      return
c
c     %---------------%
c     | End of igraphdnconv |
c     %---------------%
c
      end
